mathematics

Richard Kadison

Richard Kadison is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Richard Kadison rather than just read about it. In short: Richard Vincent Kadison (July 25, 1925 – August 22, 2018) was an American mathematician known for his contributions to the study of operator algebras. Career Born in New York City in 1925, Kadison was a Gustave C.

Key takeaways

Richard Kadison belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Richard Kadison to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Richard Kadison from memory before moving on to harder problems.

Reference excerpt

Richard Vincent Kadison (July 25, 1925 – August 22, 2018) was an American mathematician known for his contributions to the study of operator algebras.

Career Born in New York City in 1925, Kadison was a Gustave C. Kuemmerle Professor in the Department of Mathematics of the University of Pennsylvania. Kadison was a member of the U.S. National Academy of Sciences (elected in 1996), and a foreign member of the Royal Danish Academy of Sciences and Letters (elected 1974) and of the Norwegian Academy of Science and Letters. He was a 1969 Guggenheim Fellow. Kadison was awarded the 1999 Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society. In 2012, he became a fellow of the American Mathematical Society.

Personal life Kadison served as an officer in the merchant marines for several years after 1943. He was a skilled gymnast with a specialty in rings, making the 1952 US Olympic Team but later withdrawing due to an injury. He married Karen M. Holm on June 5, 1956, and they had one son, Lars. Kadison died after a short illness on August 22, 2018.

Selected publications

Books with John Ringrose: Fundamentals of the Theory of Operator Algebras 2 vols., Academic Press 1983; new edition, Fundamentals of the theory of operator algebras: Elementary theory, Vol. 1, 1997 Fundamentals of the theory of operator algebras: Advanced theory, Vol. 2, 1997 AMS 1997 with John Ringrose: Fundamentals of the theory of operator algebras, III-IV. An exercise approach, Birkhäuser, Basel, III: 1991, xiv+273 pp., ISBN 0-8176-3497-5; IV: 1992, xiv+586 pp., ISBN 0-8176-3498-3

PNAS articles Kadison, R. V. (1998). "On representations of finite type". Proc Natl Acad Sci U S A. 95 (23): 13392–6. Bibcode:1998PNAS...9513392K. doi:10.1073/pnas.95.23.13392. PMC 24829. PMID 9811810. with I. M. Singer: Kadison, R. V.; Singer, I. M. (1952). "Some Remarks on Representations of Connected Groups". Proc Natl Acad Sci U S A. 38 (5): 419–23. Bibcode:1952PNAS...38..419K. doi:10.1073/pnas.38.5.419. PMC 1063576. PMID 16589115. with Bent Fuglede: Fuglede, B.; Kadison, R. V. (1951). "On a Conjecture of Murray and von Neumann". Proc Natl Acad Sci U S A. 37 (7): 420–5. Bibcode:1951PNAS...37..420F. doi:10.1073/pnas.37.7.420. PMC 1063392. PMID 16578376. with Zhe Liu: Kadison, Richard V.; Liu, Zhe (2014). "A note on derivations of Murray–von Neumann algebras". Proc Natl Acad Sci U S A. 111 (6): 2087–93. Bibcode:2014PNAS..111.2087K. doi:10.1073/pnas.1321358111. PMC 3926033. PMID 24469831. Kadison, R. V. (2002). "The Pythagorean Theorem: II. The infinite discrete case". Proc Natl Acad Sci U S A. 99 (8): 5217–22. Bibcode:2002PNAS...99.5217K. doi:10.1073/pnas.032677299. PMC 122749. PMID 16578869. Kadison, R. V. (2002). "The Pythagorean Theorem: I. The finite case". Proc Natl Acad Sci U S A. 99 (7): 4178–84. Bibcode:2002PNAS...99.4178K. doi:10.1073/pnas.032677199. PMC 123622. PMID 11929992. Kadison, R. V. (1957). "Irreducible Operator Algebras". Proc Natl Acad Sci U S A. 43 (3): 273–6. Bibcode:1957PNAS...43..273K. doi:10.1073/pnas.43.3.273. PMC 528430. PMID 16590013. Kadison, R. V. (1955). "On the Additivity of the Trace in Finite Factors". Proc Natl Acad Sci U S A. 41 (6): 385–7. Bibcode:1955PNAS...41..385K. doi:10.1073/pnas.41.6.385. PMC 528101. PMID 16589685. Kadison, R. V. (1955). "Multiplicity Theory for Operator Algebras". Proc Natl Acad Sci U S A. 41 (3): 169–73. Bibcode:1955PNAS...41..169K. doi:10.1073/pnas.41.3.169. PMC 528046. PMID 16589638. with Bent Fuglede: Fuglede, B.; Kadison, R. V. (1951). "On Determinants and a Property of the Trace in Finite Factors". Proc Natl Acad Sci U S A. 37 (7): 425–31. Bibcode:1951PNAS...37..425F. doi:10.1073/pnas.37.7.425. PMC 1063393. PMID 16578377.

References

External links Richard Kadison at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Richard Kadison

Start with the simplest possible case. Write down what Richard Kadison claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Richard Kadison before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Richard Kadison ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Richard Kadison

In research: Richard Kadison appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Richard Kadison in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Richard Kadison is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1925 births, 2018 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Richard Kadison outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Richard Kadison in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Richard Kadison means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Richard Kadison in simple terms?

Richard Vincent Kadison (July 25, 1925 – August 22, 2018) was an American mathematician known for his contributions to the study of operator algebras. Career Born in New York City in 1925, Kadison was a Gustave C.

Why does Richard Kadison matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Richard Kadison?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Richard Kadison.